In the wake of the ongoing deregulations of the electric power markets, load transmission and wheeling of power from distant generators to local consumers has become common practice. Due to the competition between power producing companies and the emerging need to optimize assets, increased amounts of electric power are transmitted through the existing networks, frequently causing congestion due to transmission bottlenecks. Transmission bottlenecks can be handled by introducing transfer limits on transmission interfaces. This improves system security, but it also implies that more costly power production has to be connected while less costly production is disconnected from the grid. Thus, transmission bottlenecks can have a substantial cost to the society. If transfer limits are not respected, system security is degraded which may imply disconnection of a large number of customers or even complete blackouts in the event of credible contingencies.
An underlying physical cause of transmission bottlenecks is often related to the dynamics of the power system. A number of dynamic phenomena need to be avoided in order to certify sufficiently secure system operation, such as loss of synchronism, voltage collapse and growing electromechanical oscillations. In this regard, electrical transmission networks are highly dynamic and employ control systems and feedback to improve performance and increase transfer limits.
With reference to unwanted electromechanical oscillations that occur in parts of the power network, they generally have a frequency of less than a few Hz and are considered acceptable as long as they decay fast enough. They are initiated by, for example, normal changes in the system load or switching events in the network possibly following faults, and they are a characteristic of any power system. However, insufficiently damped oscillations may occur when the operating point of the power system is changed, for example, due to a new distribution of power flows following a connection or disconnection of generators, loads and/or transmission lines. In these cases, an increase in the transmitted power of a few megawatts (MW) may make the difference between stable oscillations and unstable oscillations which have the potential to cause a system collapse or result in loss of synchronism, loss of interconnections and ultimately the inability to supply electric power to the customer. Appropriate monitoring and control of the power system can be helpful for a network operator to accurately assess power system states and avoid a total blackout by taking appropriate actions such as the connection of specially designed oscillation damping equipment.
It has been found that electromechanical oscillations in electric power networks also take the form of a superposition of multiple oscillatory modes. These multiple oscillatory modes create similar problems to the single mode oscillations and thus have the potential to cause a collapse of the electric power network. Furthermore, in situations where a Power Oscillation Damping (POD) controller is used to stabilize a single selected oscillatory mode, this may often have the effect of destabilizing the other oscillatory modes present, for example, a second dominant mode, which is subsequently damped less than the first dominant mode.
Generally, power networks utilize so-called lead-lag controllers to improve undesirable frequency responses. Such a controller functions either as a lead controller or a lag controller at any given time point. In both cases, a pole-zero pair is introduced into an open loop transfer function. The transfer function can be written in the Laplace domain as:Y=s−zXs−p where X is the input to the compensator, Y is the output, s is the complex Laplace transform variable, z is the zero frequency, and p is the pole frequency. The pole and zero can both be negative and generally are both negative. In a lead controller, the pole is left of the zero in the Argand plane, |z|<|p|, while in a lag controller |z|>|p|. A lead-lag controller includes a lead controller cascaded with a lag controller. The overall transfer function can be written as:Y=(s−z1)(s−z2)X(s−p1)(s−p2)
Generally, |p1|>|z1|>|z2|>|p2|, where z1 and p1 are the zero and pole of the lead controller, and z2 and p2 are the zero and pole of the lag controller. The lead controller provides a phase lead at high frequencies. This shifts the poles to the left, which enhances the responsiveness and stability of the system. The lag controller provides phase lag at low frequencies which reduces the steady state error.
The precise locations of the poles and zeros depend on both the desired characteristics of the closed loop response and the characteristics of the system being controlled. However, the pole and zero of the lag controller should be close together so as not to cause the poles to shift right, which could cause instability or slow convergence. Since their purpose is to affect the low frequency behavior, they should be near the origin.
Electric power transmission and distribution systems or networks include high-voltage tie lines for connecting geographically separated regions, medium-voltage lines, and substations for transforming voltages and switching connections between lines. For managing the network, it is known in the art to utilize Phasor Measurement Units (PMU). PMUs provide time-stamped local information about the network, such as currents, voltages and load flows. A plurality of phasor measurements collected throughout the network by PMUs and processed at a central data processor provide a snapshot of the overall electrical state of the power system.
The article “Application of FACTS Devices for Damping of Power System Oscillations”, by R. Sadikovic et al., Proceedings of the Power Tech Conference 2005, Jun. 27-30, 2005, St. Petersburg RU, is incorporated herein for all purposes by way of reference. This article addresses the selection of the proper feedback signals and the subsequent adaptive tuning of the parameters of a power oscillation damping (POD) controller in case of changing operating conditions. It is based on a linearized system model, the transfer function G(s) of which is expanded into a sum of N residues:
      G    ⁡          (      s      )        =            ∑              i        =        1            N        ⁢                  ⁢                  R        i                    (                  s          -                      λ            i                          )            
The N eigenvalues λi correspond to the N oscillation modes of the system, whereas the residue Ri for a particular mode gives the sensitivity of that mode's eigenvalue to feedback between the output and the input of the system. It should be noted that in complex analysis, the “residue” is a complex number which describes the behavior of line integrals of a meromorphic function around a singularity. Residues may be used to compute real integrals as well and allow the determination of more complicated path integrals via the residue theorem. Each residue represents a product of modal observability and controllability. FIG. 1 provides a graphical illustration of the phase compensation angle φc in the s-plane caused by the POD controller in order to achieve the desired shift λk=αk+j·ωk of the selected/critical mode k, where αk is the modal damping and ωk is the modal frequency. The resulting phase compensation angle φc is obtained as the complement to +π and −π, respectively, for the sum of all partial angle contributions obtained at the frequency ωk starting from the complex residue for mode λk, input I and output j, Resji(λk), all employed (low- and high-pass) prefilters. φR is the angle of residue and φF is the phase shift caused by the prefilters.
Thus, it is known to utilize local feedback signals in power network control systems. However, it is considered that power network control systems based on remote feedback signals may lead to substantial improvements in terms of damping unwanted electromechanical oscillations. However, there is a disadvantage associated with remote feedback signals. For instance, remote signals are acquired by PMUs at distant geographical locations and sent via communication channels, which are potentially several thousand kilometers in length, to the controller. The remote signals may also pass through a wide-area data concentrating platform. Consequently, there may be permanent time delays in the feedback loop. It is known that such time delays may destabilize the feedback loop.